Numbers, to the eye of the common man, is by far the most important thing in life, it surmises in itself a multitude of things that happens and might be said that its the determinant of people’s life. It starts from money, benefits, clothes to more complicated terms such as wife/wives, computation, sciences, economy and so on. G.K. Chesterton, a very celebrated English literature person, writes in his book ‘The man who was Thursday’- “It may be conceded to the mathematicians that four is twice two. But two is not twice one; two is two thousand times one”. He very confidently writes “as conceded to the mathematicians”, of course it is understandable that he was talking about a more general perspective, but I chose this piece of quote for the reason that people make use of numbers in such freedom, as though they are an entity that is embedded in them. Before I throw more entangled arguments about numbers and their mystery, I shall quote a more sarcastic and in ways, a funny quote- “Natural numbers are better for your health.” People have a very casual mentality of treating numbers, they are so accustomed to it that one does not see the underlying mystery and paradoxical nature of numbers. To this, I sternly blame every academic programme that originates with the history of numbers, though I agree on the fact that people who have worked on the field need to be mentioned for their extraordinary line of thought, I disagree that that is what kids should start learning numbers from. If one is introduced to the startling mystery these mathematical entities hold, there may be a more interactive interest in mathematics, what I mean is that that people would understand the deep mystery numbers hold in themselves.
Consider a square of each side 1( in any metric system of measure of length), something we should be easily able to achieve in physical reality, now, the length of the line that connects any two vertices of this square has a very strange value, in our considered example, it is squareroot of 2. A very easy calculation given one knows how to apply the pythogoras theorem. Well, any calculator can possibly tell you what that number is, but the question being, do you understand the number? Do yu understand the physical sense the number portrays? Have you bothered to question WHY it is so? To peck brains, I would suggest you brush up on your knowledge of the real number system, why you ask? Well, if you understand the entirety of the simple paradox I am pointing toward, squareroot of 2 as a number is up to infinite length after the decimal, i.e. 1.4214….. and can go as long as you your patience wears or your computer’s capability to find till. But the diagonal of a square is a definitive physical reality, it exists, we can measure it, infact we all might have, at points in school if you had geometry. To the student of mathematical and physical sciences this may lead to two questions, two unanswerable questions, first- how can a theoretical, rather imaginative structure of computation describe a physical reality? Well, that is the beauty of mathematics. Second- this is something most people miss, it seems very non intuitive but it is true, I have experimented this myself and the results are most shocking. The fact that we have drawn a square and computed the length of the diagonal only means we have done it as much as it seems accurate to the naked eye. What this piece of puzzle leads you toward is the fact that if we had better methods, we could make the square more precise, how much you ask? Well, as much as the number expands, this is a very non intuitive idea but a very interesting one, the fact that we have joined opposite vertices of the square only means we have done it as far accurate as we can seem to see and think. Theoretically, this position is very hard to find, we may only approximate this and hence the complicated number related to it.
Why are numbers significant? Trivially, numbers have a part to play in almost every situation in our routine. But going further, with the ability to think of a number system that can be used for computation of any physical reality, comes a great idea, one which is often mistaken to be a derivative of the physical sciences- error propagation. In the 17th century, when the rationals and irrationals were known, mathematicians who had a core understanding of calculus felt that to explain mathematically the observable reality, the rationals and irrationals were a very ill serving number system, in situations their combination(in the most crude way of putting it) the real number system was also faced with the same consequence. All these concepts are a layered within themselves, often unasked, the disadvantage of asking the “why” question. What is questionable is how we have a desire for definitiveness in our views, while naturally all there exists is approximation and an underlying chaos. The complex number system is the most descriptive number system, but alas, not a very useful physical application. But as a computational tool to be used, these are the most powerful of numbers. Hence the conundrum, and a puzzling one at that- are numbers universally existing and we have merely discovered them? Or are they a human invention and we have the greatest gift analytically analysing our surroundings? Take a journey through the numbers, they are as scenic and beautiful as a holiday destination. I shall surmise with a quote that led me to think about this-” God made the integers; all the rest is the work of Man.” by Leopold Kronecker.